perceiving musical stability the effect of tonal structure, rhythm, and musical expertise

7/24/2019 Perceiving Musical Stability the Effect of Tonal Structure, Rhythm, And Musical Expertise

1/15

Journal

of Experimental Psychology:

Human

Perception and

Performance

1997, Vol.

23, No. 3,808-822

Copyright 1997 by the American Psychological Association, Inc.

00%-15

PerceivingMusical Stability:

The

Effect

of

TonalStructure,

Rhythm,

andMusical Expertise

Emmanuel

Bigand

Universitfi

deBourgogne

The

goal

of thisstudywas to investigate

several

factorsthat

determine

musicalstabilityin

unaccompanied tonalmelodies.Following M. R.Jones's (1987)theoryofdynamic

attending,

theauthorassumed that strongly accentedtonesact as stablemelodic

reference

points.Three

mainresults

wereobserved:

(a)

tonalstructure,

rhythm,and

melodic

factors(i.e.,

pitch skips

or

change in melodic contour) all contributed to

defining

the

stability

experiencedon the

melodictones;(b) alinearcombination of 5 melodic and

rhythmicfeatures

provided a good

fit to thestability

ratings;

and (c)

some

of

thesefeatures

contributed

differently,depending

on the

extent

of musicalexpertiseof the

participants.

The

results

are

interpretedwithin

C. L.

Krumhansl's

(1990) modelof

tonal perception

andJones'stheory of

dynamic

attending.

Musical

pieces

are most commonly perceived to be

sound

structures matevolvedynamically through

time:

Atcertain

points in a musicalpiece,we can evaluate whether the piece

is

finished, when

it

will reach

its

final point,

what the

forthcomingevents should be, and when they should occur

intime. Thepresentstudy investigated severalfactorsthat

cause musical

piecesto

sound like dynamic structures

for

listeners.

According to music theorists, the impression that music

progressesdynamically through time stems primarily

from

thesequence of stable and unstable events in time (Lerdahl

&Jackendoff, 1983; Meyer, 1956, 1973; Schenker,1935).

Ina given musical context, some events (tones or chords)

are perceived to be more

stable

than others. Unstable events

instill

strong musical tensions that generate

the

expectancy

thatmore stable events will follow. During the past decade,

several empirical studies showed that musical stability and

expectancy

are

influenced

by

several factors including

me-

lodic

interval sizes

(Bigand, Parncutt,

& Lerdahl, 1996;

Carlsen, 1981; Unyk& Carlsen, 1987), melodic contour

(Schmuckler,1989,1990),rhythmic features

(Boltz,

1989a,

1989b;Jones, Boltz, & Klein, 1993; Palmer &Krumhansl,

1987a, 1987b), and tonal and harmonic structures (Bha-

rucha&Stoeckig,1986, 1987; Bigand etal.,1996; Palmer

& Krumhansl, 1987a, 1987b; Schmuckler,

1989,

1990;

Schmuckler & Boltz, 1994). To date, none of these studies

hasmanipulated these factors simultaneouslytodetermine

their relative weighting. Therefore,

the

first goal

of the

present study was to determine how tonal structureand

rhythmact in

combination

toaffect theperceived musical

stability

in

relatively long

and

complex melodies.

The

sec-

ondgoal was to test a quantitative model designed to predict

IthankM.-C.Botte, C.Drake,C.Krumhansl,P. Lemaire, S.

McAdams,

and B.Repp for their

insightful comments,

which

greatly improved thearticle.

Correspondence concerningthis

article

should be addressed to

EmmanuelBigand,

LEAD-CNRS

URA1838,6 Boulevard Gab-

riel,

Facult6

des

Sciences,F-21000Dijon,France.

Electronic

mail

may be

sent

viaInternetto [email protected].

the degree of stability experienced with each tone of a

melody.

Let

us

considereach

of these melodic and

rhythmic

factors in

greater detail

and see how we can

quantify their

respective effects.

Tonal Hierarchy

Musical stability isrelated,in part, to thescaledegree of

the

tones

in the

melody's underlying diatonic scale. Accord-

ing

to

Meyer

(1956),

Inthe

majormode

in Western

music

the tonic

tone

is the

tone of ultimate rest toward whichall other

tones

tend to

move.

On the

next

higher

level

the third and

fifth

of the

scale,

though active

melodic

tones

relative to the

tonic,

join

the

tonic

as structural

tones; and all the

othertones,whether

diatonic or

chromatic,tendtoward one of these,(pp. 214-215)

Sucha tonal hierarchy has received a great deal of empirical

support:

Once the key of a musical context is recognized,

the 12 tones of the chromatic scales are perceived in a

hierarchy of stability (Frances, 1958/1988; Krumhansl,

1990).

In

major

key

contexts,

the tonic

(firstscale

degree) is

perceived

to be

more stable than

the

dominant(fifth scale

degree), which

in

turn

is

perceived

to be

more stable than

the mediant (third scale degree). Tones of the other scale

degrees

are

perceived

to be

less stable

but

more stable than

nondiatonic

tones.

Stable tones

in a

given musical context

act as

cognitive

reference points to which the other tones are anchored

(Bharucha,1984; Krumhansl, 1990; Laden, 1994). Chang-

ing the key of thecontext leadstochangesinthesereference

points

so

that events that were stable

in a

given context

may

become unstableinanotherkeycontext.As anexample,the

two-tone sequence

E-F

instills

a

dynamic tension

to

relax-

ationrelation in the key context of Fmajor:E is perceived

to be an

unstable tone

and F, a

verystable one. This

stability

profile maychange withthecontext.In the keycontextsof

E

major

and E

minor,

E isperceivedto be

morestablethan

F. In

these contexts,

the two

tonesdefine

a new

stability


2/15

PERCEIVINGMUSICAL

STABILITY

809

profile

becausetheyinstill

a relaxation to

tension

relation.

Changes in the musical stability of the tones are of psycho-

logical importance because they

alter

the dynamic shape of

thesequence

and, subsequently, modify

its perceptual

iden-

tity.

Indeed,

Dowling(1986)showed that changing the key

context of a six-tone melody makes that melodydifficultto

recognize. Similar results were obtained by Bigand and

Kneau(1996)with longer tone sequences.

The

connectionist model

of tonal perception developed by

Bharucha(1987)

provides

an

elegant account

for theeffects

of

key context on musical stability. In this model, the 12

tones

of thechromaticscalearelinkedtomajorandminor

chords and to major and minor keys. Tonal hierarchies are

represented by the strength of the

connections

that link tone

units

to

chord

and key

units.

Musicalstabilityis instantiated

bythe amount of activation that spreads from key units to

tone units. The more activated tone units correspond with

the more

stable

tones in a given context and vice versa.

Changing

the key

context would

modify the

amount

of

activation propagating to the tone units, so that a unit that is

strongly activated in one context would be less activated in

another.

The first

purpose

of thepresent studywas totesthow key

context effects

may

affect

the

perception

of

melodies

shar-

ing

a long set of pitches in the same sequential order. Let us

consider,for example, the

melodies

ofFigure1.Tlmelo-

dies are in A minor. To change the musical stability, the key

was

changed in T2 by altering the pitches of the first three

notes. According

to

Butler

and

Brown

(1984),the

tritone

F#-Cinstillsastrong feeling of the key of G in T2. To

maintain thiskeyinterpretation,the G#s (Numbers 1 and

20) were lowered by a

semitone.

All the remaining notes are

thesamein Tl and

T2;

theonly difference concerned their

stability. According to tonal hierarchy,

the

A in Tl (Number

2)

is a stable tonic tone, but a more unstable tone (second

scale degree) in

T2.

The B (Number 3) is an unstable second

scale degreein Tl, but amore stable third degreein

T2.

By

contrast,

the C

(Number

4) is a

relatively

stable

third

degree

in

Tl,but a more unstablefourthdegree inT2.By changing

a few

notes,

the

stability

of the

melodic tones

has

been

completely

inverted

fromTl to T2.

Rhythmic

Structures

Thestability

of

tones

is not

determined entirely

by the

tonal hierarchy of the

melody's

underlying key. Varying

some acoustic features

(i.e.,

timbre, intensity, duration) can

alter stability and, thus, modify

perceptionof thepiece.

This

suggests that other features should be included in a model of

tonal hierarchy so as to account for the perception of mel-

odies

(Boltz,

1989b;Laden, 1994).

Generally, the stability of a note depends on the rhythmic

context in which it appears. According to Lerdahl and

Jackendoff

(1983),

rhythmic structures have a double

func-

tion.First,they divide the

piece

into groups and, then, they

addrhythmic values to the tonal hierarchies to determinethe

musical

function

of the events contained in the groups.

234567 8

9101112131415 16171819202122 23

Stop

notes

1 23 4567 8

9101112131415

16171819202122 23

T1R2

1 2 3 4 5 6 7 891011121314 15161718192021

2223

Stop

notes

1234567

891011121314 15161718192021

2223

Figure 1.

Four melodies used

inExperiment1. The tonal structure (T) varies

from

Tl to Tl, and

the rhythmic structure(R) variesfromRlto R2.


3/15

810

BIGAND

From

a

cognitive point

of

view,

the

function

of

rhythm

may

be to

create temporal accents that capture

the

listeners'

attention and emphasize certain relationships among the

tones of a melody

(Boltz,

1991a, 1993a, 1993b; Jones,

1987). Jones, Boltz,

and Kidd

(1982) reported that

it is

easier

to discern pitch changes in a melody when these

changes occur on temporal accents. Changing the rhythm of

a

melody modifiesthemannerinwhich attentionis

guided

through time, such that tones that capture attention in one

rhythmic

context

failto do so in

another rhythmic context

andvice versa (Boltz,1989a,1991a;Jones& Boltz, 1989;

Jones

&

Ralston, 1991;

Jones,

Summerell,

&

Marshburn,

1987).

The second purpose of the present experiments was to

investigate how a change in rhythm affects the stability

perceived with each tone of long melody. I assumed that

tones that

receive

rhythmic accents should

be

perceived

to

be stable melodic referencepointsbecause they can capture

the

listeners' attention. Changing

the

rhythm

of a

melody

wouldshiftthe rhythmic accents and then alter the overall

musical

stability profile for this melody. Previous results

reported

by

Palmer

and

Krumhansl

(1987a,

1987b;

see

also

Bigand, 1993) and, more recently, by Laden(1994)sup-

ported this assumption.

Integration

of thePitchand Rhythmic Structures

Given that both pitch and rhythmic structures govern the

perception

of

tonal melodies,

the

third goal

of the

present

study

was to

investigate

how

these structures

act in

combi-

nation.

Peretzand

Kolinsky (1993) distinguished

two ac-

counts of theprocessing

of

pitchandrhythmic structures.

One isthat pitchandrhythmare twoseparate perceptual

components,

so

that changing

one of

them

in a

melody

would

not

necessarily interfere with

the

processing

of the

other. This

two-component

model

was

supported

by

several

studies in neuropsychology (Peretz, 1990; Peretz & Kolin-

sky,

1993; Peretz &

Morais,

1989) and other empirical

studies

(Halpern, 1984; Monahan & Carterette, 1985;

Monanan, Kendall, & Carterette, 1987; Palmer &

Krum-

hansl,1987a,1987b; Smith & Cuddy,1989).

A

second possibility

is

that pitch

and

rhythm

are

pro-

cessed integrally,

so

that

a

change

in one

affects

the

per-

ception

of the

melody

as a

whole. This single-component

modelwassupportedbyseveral studies askingthepartici-

pants

to

recallmelodies (Boltz, 1991a; Boltz

&

Jones, 1986;

Deutsch,

1980), torecognize

melodies (Boltz,

1993a;

Jones,

Summerell, & Marshbum, 1987; Jones & Ralston,1991),to

evaluate

how complete a melody is (Boltz, 1989a, 1989b),

or to

estimate

the

duration

of

melodies (Boltz, 1991b,

1993b; Jones, Boltz, & Klein, 1993).According to Boltz

(1989a, 1989b), the strongest evidence for a single-

component model comesfromthe presence of interactions

between pitch and rhythmic structure. For example, Boltz

(1989b)

foundthat melodies were judged

to be

more com-

plete when ending

on the

dominant tone than

when

ending

on

the

mediant tone,

but

only when

the

dominant tones were

rhythmicallyaccented throughout

the

melody.

The

reverse

phenomenon was observed when the mediant tones were

rhythmically accented.

In a

similar vein, Boltz (1989a)

argued that thedifferencein musical relaxation provided by

certain pitch intervals may vary strongly depending on

whether or not these intervals occur on time, relative to the

preceding temporal context. Consistent data were reported

bySchmuckler and Boltz(1994)with chord

sequences

and

by

Boltz (1993a) in a recognition task. The two sets of

conflicting results are

difficult

to integrate within a single

framework.

A

third possibility suggested by Peretz and Kolinsky

(1993)is that pitch and rhythm are treated independently in

an earlier stage of melodicprocessingand are then fused

into

a

unified dimension

in a

second stage

of

processing.

However, the question remains of specifying whether inte-

gration that may occur at a second stage of processing relies

on an additive

or

on an interactive combination ofboth

structures. No definite answer to this question seems to be

available currently. Thus,

the

third purpose

of the

present

studywas to investigate this issuefurtherin an experimental

design that

differed

in

several regards

from

those that

are

commonly used.

First,two rhythmic structures werecrossedwith two pitch

structures

in a 2 X 2

factorial design. Second,

the

melodies

differed

in

tonal structure

but not in

melodic features (i.e.,

pitch skips and melodic contour), which were kept constant

(see Figure 1). Third, the degree of musical stability expe-

rienced

by

listeners was registered at several locations in the

melodies. Such a design allowed us to determine whether

the

interactive effect occurs

on

only

one or two

specific

tonesof themelodyor on themajorityof themelodic tones.

Predicting

Perceived Musical Stability

As

stated by Boltz(1989b),regardless of their additive or

interactive nature, significanteffects ofboth rhythmicand

tonal structures would demonstrate

"the

need to incorporate

dynamic pattern influences into models of tonal perception

(p.12).Thefourthgoalof thepresentstudywas toaddress

this issue in defining a model that would predict the effect

of several melodic

and

temporal factors

on the

perceived

musical stability. The rationale for the present model was

provided primarily

by

Jones (1987)

and

Jones

and

Boltz

(1989).

According to Jones (1987), pitch and rhythmic structures

display several kindsofmelodic (in) and temporal (t) ac-

cents. The manner in which these accents are temporally

phased creates a

unified

accent structure (called Jointaccent

structure) that dynamically orients

the

listeners'attention.

According

to

Jones

and

Boltz (1989)

the

dynamic

shapeof

a musical sequence

refers

to the influence that thejoint

accent

structure

has on the

attentionaltrajectories developed

during

the listening of thepiece.The main property of a

joint accent structure is that it contains melodic markers of

different strengths: coupled

or

temporally coincident

ac-

cents (m plus f) yield stronger markers than

do

single

accents

(m

or t), (Jones, 1987,p.625).Thestrengthof a

marker

was

determined

by the

number

of

accents that

co-


4/15

PERCEIVING MUSICAL STABILITY

811

incide in time (Jones &

Boltz,

1989).Changingthe

rhythm

ofa

melody changes

the

accent coupling, such

that

strong

markers in one rhythmic structure may be weak markers in

another and

vice versa. Consequently, these changes should

alter

the

dynamic shape

of the

sequence

in

that they

modify

the

modes of attentional following in listeners. Changing

thepitch structure provokes similar changes in the strength

ofthe markers in thejointaccent structure and, thus, in the

dynamic shape of the sequence.

In the

present study,

the

influence

of

several melodic

rhythmic features

on the dynamic shape of a melody was

addressed by considering the

effects

of these

features

on the

perceived musicalstabilityprofiles. Stability profilerefers

to the alternation of stable and less stable tones in the

melody. Strong markers were assumed to act as very stable

melodic reference points because of the presumably strong

attraction

that they exert on the

listeners' attention.

The

computed strengths of accentuation for each tone of a mel-

ody should then provide a good fit to the perceived stability.

Following Jones (1987),

Jones

and Boltz

(1989),

Se-

rafine,

Classman,

and

Overbeeke

(1989), and Bigand

(1993), five predictors were used: tonal

weight,

duration

weight, metric weight, interval size weight, and melodic

contour weight. The tonal weights, defined according to

Krumhansl's(1990)model of tonal perception,

reflect

the

importance of each tone in the tonal hierarchy of the mel-

ody's

underlying key. Following

Krumhansl

and

Kessler's

findings

(1982,Experiment 2), when part of a musical piece

suggests

a new key

(temporary modulation),

the

present

model assigns to this part of thepiecethe key profile values

of

this

new

temporary

key

(see Experiment

2). How the

tonal

weights (TW) were defined

for the

melodies

of Ex-

periment 1 (Figure 1) is displayed in Table 1, where they are

shown to come from the major and minor key profiles

reportedby

Krumhansl

and

Kessler (1982)

and Krumhansl

(1990, p. 30). Because the main key of the

Tl

melodies is

A

minor, the values of Tl melodies are those of

Krum-

hansl's A minor

profile.

The values of T2 melodies are

those of KmmhansFs G

major

profile. Illustratively, the

tonal weight

of the A

(number

2 in

Figure

1) is

6.33

in Tl

because A is the tonic tone. The tonal weight for the same

A

in T2 is 3.48 because the A is the second degree in this

key

context and so on. Changes in values reflect the hypo-

thetical changes in musical stability created by the two key

contexts in

which

the tones appear. Not surprisingly, there

was

a high negative correlation between the Tl and the T2

values, K21)

= -.81, p


5/15

812

BIGAND

melodic interval was computed

(MIW

valuesin

Table

1).

To account for thepotentialinfluenceof change inmelodic

contour, a value of 1 was assigned to the tones onwhicha

change in

contouroccurs.

Avalueof 0 was

assigned

in the

othercases

(MCW

values in Table 1).

To summarize, we hypothesizethatseveral

factors

may

affect theperceptionofstability.Two ofthese(i.e.,tonal

structure and

rhythm)

were varied systematically in die

following

experiments

and theothers(intervalsize,

melodic

contour)

werekeptconstant.

Three

main

assumptions

were

made:

1.

changing

the

tonal structure

of a

melody

by

modifyingonly

a few

pitches should stronglyaffect

the

stability

for the

majorityof the

other

tones;

2. changing the rhythmic structure should also

affect

the

stability of themelodic tones;and

3. acombinationof fivekindsofmelodic andrhythmicac-

cents(i.e.,tonal, duration, metric, interval size, and me-

lodic contour weights) should predict the perceived

stability.

Inaddition,giventhat someofthesefactors rely onmore

superficial

features(duration,melodicintervalsizes,change

in melodic contour) than others (tonal and metric struc-

tures), some

may be

more important

for

musicians

and

some

for nonmusicians. Thus, testing

these

factors

provided

an

opportunity

to investigate theeffectof

musical expertise

on

theperceptionofmusicalstability.

Experiment1

Method

Participants.

Forty music teachers (hereinafter referred

to as

musicians)volunteered toparticipatein theexperiment.Allheld

qualificationsfrom a French Music Conservatory and had received

atleast

10

years

of

intensive training

in

music(i.e.,music theory,

ear

training,

and

instrumental performance). Fortycollege-age

students(hereinafter referred to as nonmusicians) also took part

hi

theexperiment.Theyhadnever playedaninstrumentnorstudied

music.Allwere students of psychology and participated in the

experiment as

volunteers.

Material.

Four melodies T1R1, T1R2, T2R1,

and T2R2

were

defined(Figure 1). The

Tl

melodies

differed

from the T2 melodies

by

the key

context induced

by the

firstmelodic tones. Following

Palmer and

Krumhansl (1987a, 1987b),

the R2

melodies were

defined by

shifting

the

rhythmic structure

of

Rl

by one

eighth

note. Consequently, mostof thetones thatfallon astrong metric

beat

in Rl

fall

on a

weak metric beat

in R2 and

vice versa. Several

tones with

a

long duration

in Rl

have

a

short duration

in R2 and

viceversa. These four melodies were segmented into 23 frag-

ments.Each segment started

at the

beginning

of the

melody

and

stopped on a

different

note called a slop note.Forexample, in

T1R1, thefirstfragmentstoppedonG#,thesecondon A, and so

on.

The 23 fragments

were played with sampled piano sounds

produced

by the

EMT1O Yamaha Sound Expander

at a

tempo

of

80

quarter notes

per

minute.

The Yamaha

sampler

was

controlled

through a

MIDI interface

by a

Macintosh computer running Per-

former

software. Velocity,

aparameter related to the

force

with

which a key is

struck,

was

held constant

for all

pitches.

The

participants

were allowedtoadjusttheoutputof theamplifierto a

comfortable

level. There

was no

silence

between

the

offset

of a

tone and the onset of the succeeding tone.

Task.

The

participants' task, similar

to

that used

by

Palmer

and

Krumhansl(1987a,

1987b),

consistedof

evaluating

the

musical

stability on each stop note using a judgment scale ranging from 1

(very

low

stability)

to 7

(very great stability).

In a preliminary

session,the participantslistenedto musical examples having dif-

ferent

degrees

of

stability. They were told that strong stability

at

the end of a fragment

evokes

the

feeling that

the

melody could

naturallystop

at

this point.

On the

other hand,

low

stability evokes

the

feeling

that there must be a continuation of the melody.

Because stability

may be

varied

in

subtle ways

in

musk,

the

participants were encouraged to use all thedegreesof the judgment

scale.In addition, at the end of the experiment, the musicians were

required

to

identify

the key of the

melody that they

had

listened

to

and toidentifyitsmeter (i.e., theyhad todrawthe barlineson a

score).

Design and procedure. Four independent groupsof 10partic-

ipants each were assigned

to the

fourconditions defined

by

cross-

ingthe two independent variables: Key context (2) x Rhythm (2).

Each participant gave

a

rating

for

each

of the 23

stop notes

of

only

one

melody.

Theparticipants

were seated

in

groups

of

two, each

in

front

of a

MIDI keyboard, connected

to the

computer, which

recorded their answers. Seven keys corresponded to the 7 points of

thejudgment

scale.

Before running the experiment, the partici-

pants practiced evaluation of musical stability with 12 melodic

fragments. No

feedback

was

provided

unless

they used

the

scale

in

thereverse order.Theexperiment started withthe

fragment

ter-

minating on

Stop Note

1. The

participants

had 8 s to

give their

stability judgment.

After

that,

the fragment

terminating

on

Stop

Note

2 was

played, then

the

fragmentending

on

Stop Note

3, and

so on.

This makes

the

judgments

collectedon

stop notes compa-

rable because

all the

stop notes were judged when

they

were

first

heard. As observed by Bigand

(1993,

Experiment 1) random

presentation

of the fragments greatly confuses the participants

because it

oftenappears that

a

shortfragmentfollows

a

longer one.

Inthis case,

the

degree

of

completeness

is

defined

not

only

by

musicalstabilitybutalsoby the

listener's

knowledgeof thecon-

tinuation of the melody. As a consequence, the participants (no-

tably

the

nonmusicians) tended

to

give higher

ratings of

stability

formusicalfragments

of

increasing duration. This suggested that

for

them,

regardless of the

musicalfunction

of the

last tone,

the

longer

the fragment, the

higher

its

degree

of

completeness. This

linear tendencywas notobserved whenthe fragmentswere pre-

sented

in a

sequential order (Bigand, 1993, Experiment

2).

Results

Participantagreement.

To

assess

interparticipant

agree-

ment,

the Kendall

coefficient

ofconcordancewas computed

separately

for the

musicians

and the nonmusicians in

each

experimental situation.Theobserved coefficients were all

significant (p


6/15

PERCEIVING

MUSICAL

STABILITY

813

indicating

the

reliability

of the

experimental method.

The

lowest coefficientwasobservedfor themusiciansinT1R1,

r(21)

= .77,p


7/15

814

BIGAND

Table2

Correlation

(Pearson r) ComparingTl and T2Ratings

WithKrumhansl s Key Profiles

r for.

Participants

Musicians

Nonmusicians

Key

A

minor

Gmajor

Aminor

G

major

Tl

.69**

-.45*

.53**

-.28

T2

-.54**

.58**

-.42*

.40

*p


8/15

PERCEIVING MUSICAL STABILITY

815

Musicians Nonmusicians

Strong

beat

oWeak

beat Strong beat

oWeak

beat

notes

Z 3 4 5 6 9 1 11 12 13 16 17 18 19 2 3 4 S 6 9 1 11 12 13 16 17 18 19

2

Musicians

Nonmusicians

Quarter

note oEighth note Qyarternote

o

Eighth note

14

5

21

Figure

3.

Effects ofmetric(a) and

duration

(b)on

musical stability.

average ratings. However, additional analysis revealed a

significant interaction between tonal weights and the

extent

of

musical expertise,

t

= 3.22,

p

perceiving musical stability the effect of tonal structure, rhythm, and musical expertise

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